Musical ratios in sounds from the human cochlea.

Abstract

The physiological roots of music perception are a matter of long-lasting debate. Recently light on this problem has been shed by the study of otoacoustic emissions (OAEs), which are weak sounds generated by the inner ear following acoustic stimulation and, sometimes, even spontaneously. In the present study, a high-resolution time-frequency method called matching pursuit was applied to the OAEs recorded from the ears of 45 normal volunteers so that the component frequencies, amplitudes, latencies, and time-spans could be accurately determined. The method allowed us to find that, for each ear, the OAEs consisted of characteristic frequency patterns that we call resonant modes. Here we demonstrate that, on average, the frequency ratios of the resonant modes from all the cochleas studied possessed small integer ratios. The ratios are the same as those found by Pythagoras as being most musically pleasant and which form the basis of the Just tuning system. The statistical significance of the results was verified against a random distribution of ratios. As an explanatory model, there are attractive features in a recent theory that represents the cochlea as a surface acoustic wave resonator; in this situation the spacing between the rows of hearing receptors can create resonant cavities of defined lengths. By adjusting the geometry and the lengths of the resonant cavities, it is possible to generate the preferred frequency ratios we have found here. We conclude that musical perception might be related to specific geometrical and physiological properties of the cochlea.